9. VERY HIGH ENERGY PHOTONS AND NON-ELECTROMAGNETIC EMISSION

The highly relativistic nature of the outflows is inferred from and
constrained by the observations of GeV photons, which indicate the need
for bulk Lorentz
factors of 102
[118,
191,
24].
Such Lorentz factors result in synchrotron spectra which in the observer
frame extend beyond 100 MeV, and inverse Compton (IC) scattering of such
synchrotron photons leads to the
expectation of GeV and TeV spectral components
[304].
While 18 GeV
photons have been observed (e.g.
[205]),
TeV photons are likely to be degraded to lower energies by
pair
production, either in the source itself, or (unless the GRB is at very
low redshifts) in the intervening intergalactic medium
[73,
92].

Besides emitting in the currently studied sub-GeV electromagnetic channels,
GRB are likely to be even more luminous in other channels, such as
neutrinos, gravitational waves and cosmic rays. For instance, nucleons
entrained in the fireball will have
100 GeV bulk
kinetic energies
in the observer frame, which can lead to inelastic collisions resulting
in pions, muons, neutrinos and electrons as well as their anti-particles.
The main targets for the relativistic baryons are other particles in the
relativistic outflow and particles in the external, slower moving
environment. The expected flux and spectrum of 1-30 GeV neutrinos and
-rays
resulting from pion decay due to interactions within the expanding plasma
depends, e.g., on the neutron/proton ratio and on fireball inhomogeneities,
while that due to interactions with the surrounding medium depends on the
external gas density and its distribution; and both depend on the Lorentz
factor. Massive progenitors offer denser targets for nuclear collisions
and a larger photon density for
p and
interactions,
leading to modification of the photon spectra. On the other hand GRB
from NS-NS mergers
would be characterized by neutron-rich outflows, leading to stronger
5-10 GeV neutrinos and photons from np collisions
[17,
32,
416].
Photo-pion signatures of
100 GeV
photons and 1014-1018 eV neutrinos may be expected
to be relatively
stronger in massive (high soft photon density) progenitors. Knowing what
fraction of GRB, if any, arise from NS mergers is vital for facilitating
interferometric gravitational wave detections, e.g. with LIGO. And,
conversely, detection with LIGO would provide important clues as to whether
short bursts are NS-NS (or NS-BH) mergers, or whether massive stellar
collapses
are asymmetric enough to produce substantial gravitational wave emission
and serve as a test of the relationship between long GRB and supernovae.

The Fermi mechanism in shocks developing in the GRB outflow can also
accelerate protons to observer-frame energies up to ~ 1020 eV
[494,
492].
Internal shocks leading to the observed
-rays
have a high comoving photon density and lead to
p
photopion production and to
100 TeV neutrinos
[501].
In external shocks due to deceleration by the external medium, the
reverse shock moving into the ejecta can produce optical photons
(Section 5.2) which result
in photopion production and
1019
eV neutrinos
[502].
Neutrinos in the TeV to EeV range may be easier to detect than those at
~10 GeV energies, due to their higher interaction cross section, with
instruments currently under construction. Such neutrinos would serve as
diagnostics of the presence of relativistic shocks, and as probes of the
acceleration mechanism and the magnetic field strength. The flux and
spectrum of
1019 eV neutrinos depends on the density of the surrounding
gas, while the
1014 eV neutrinos depend on the fireball Lorentz factor.
Hence, the detection of very high energy neutrinos would provide crucial
constraints on the fireball parameters and GRB environment.

Ultra-high energy emission, in the range of GeV and harder, is
expected from electron inverse Compton in external shocks
[304]
as well as from internal shocks
[362]
in the prompt phase. The
combination of prompt MeV radiation from internal shocks and a more
prolonged GeV IC component for external shocks
[303]
is a likely explanation for the delayed GeV emission seen in some GRB
[205].
(An alternative invoking photomeson processes from ejecta protons impacting
a nearby binary stellar companion is
[218]).
The GeV photon emission from the long-term IC component in external
afterglow shocks has been considered by
[98,
523,
95,
488,
489].
The IC GeV photon component is likely to be significantly more important
[523]
than a possible proton synchrotron or electron synchrotron component at
these energies. Another possible contributor at these energies may be
0 decay from
p
interactions between shock-accelerated
protons and MeV or other photons in the GRAB shock region
[55,
467,
137].
However, under the conservative
assumption that the relativistic proton energy does not exceed the
energy in relativistic electrons or in
-rays, and
that the proton spectral index is -2.2 instead of -2, both the proton
synchrotron and the
p
components can be shown to be
substantially less important at GeV-TeV than the IC component
[523].
Another GeV photon component is expected from the
fact that in a baryonic GRB outflow neutrons are likely to be present,
and when these decouple from the protons, before any shocks occur,
pn inelastic collisions will lead to pions, including
0,
resulting in UHE photons which cascade down to the GeV range
[94,
17,
416].
The final GeV spectrum results from a
complex cascade, but a rough estimate indicates that 1-10 GeV flux
should be detectable
[17]
with GLAST
[166]
for bursts at z 0.1.

In these models, due to the high photon densities implied by GRB
models, absorption within the GRB emission region must
be taken into account
[22,
272,
398,
364,
365].
One interesting result is that the observation of photons up to a
certain energy,
say 10-20 GeV with EGRET, puts a lower limit on the bulk Lorentz factor of
the outflow, from the fact that the compactness parameter (optical
depth to ) is directly proportional to the comoving
photon density, and both this as well as the energy of the photons
depend on the bulk Lorentz factor. This has been used by
[272]
to estimate lower limits on
300-600 for a
number of specific
bursts observed with EGRET. On the other hand, for GRB with
850,
TeV photons can escape the source
[398].

Long GRB have recently been shown to be associated with supernovae
(Section 8.2). If GRB also accelerate
cosmic rays, as suspected, then
these could leave long-lasting UHE photon signatures in supernova remnants
which were associated with GRB at the time of their explosion. One example
may be the SN remnant W49B, which may be a GRB remnant. A signature of a
neutron admixture in the relativistic cosmic ray outflow would be a TeV
gamma-ray signature due to inverse Compton interactions following neutron
decay
[209]
(see also
[13]).
Continued magnetic outflows upscattering companion photons may also
signal GRB remnants
[393].
The imaging of the surrounding emission could provide new constraints
on the jet structure of the GRB.

The recent detection of delayed X-ray flares during the afterglow
phase of gamma-ray bursts (GRBs) with the Swift satellite (e.g.
[528,
338,
360])
suggests an inner-engine origin of
these flares, at radii inside the deceleration radius characterizing the
beginning of the forward shock afterglow emission. Given the
observed temporal overlapping between the flares and afterglows,
one expects an inverse Compton (IC) emission arising from such
flare photons scattered by forward shock afterglow electrons
[490].
The jet may also IC upscatter shock break-out X-ray photons
[391].
This IC emission would produce GeV-TeV flares, which may be detected by
GLAST and ground-based TeV telescopes. The detection of GeV-TeV flares
combined with low energy observations may help to constrain the poorly
known magnetic field in afterglow shocks.

At higher energies, a tentative
0.1 TeV detection
at the 3 level of
GRB 970417a has been reported with the water
Cherenkov detector Milagrito
[12].
Another possible TeV detection
[379]
of GRB 971110 has been reported with the
GRAND array, at the 2.7
level. Stacking of data from the
TIBET array for a large number of GRB time windows has led to an
estimate of a ~ 7
composite detection significance
[9].
Better sensitivity is expected from the upgraded
larger version of MILAGRO, as well as from atmospheric Cherenkov telescopes
under construction such as VERITAS, HESS, MAGIC and CANGAROO-III
[505,
342,
201,
198,
458,
123,
222].
However, GRB detections in the TeV range are expected only for rare
nearby events, since at this energy the mean free path against
absorption on
the diffuse IR photon background is ~ few hundred Mpc
[73,
92].
The mean free path is much larger at GeV energies, and based on the
handful of GRB reported in this range with EGRET, several hundred
should be detectable with large area space-based detectors such as GLAST
[289,
523].

In the standard fireball shock model of the prompt
-ray emission,
say from internal shocks or magnetic dissipation, and also in the external
afterglow shocks, the same acceleration mechanisms which lead to the
non-thermal electron power laws implied by the observed photon spectra
must also lead to proton acceleration. Using the shock parameters
inferred from broad-band photon spectral fits, one infers that protons
can be accelerated to Lorentz factors up to
1011
in the observer frame
[494,
482],
i.e. to so-called GZK energy of
Ep ~ 1020 eV. This is interesting mainly
for "baryonic" jets,
where the bulk of the energy is carried by baryons, whereas in
Poynting-dominated jets there would be much fewer protons to accelerate.
Well below the GZK energy, protons interacting with the MeV photons
present in GRB or with thermal nucleons are above the pion production
threshold and can produce ultra-high energy neutrinos, as discussed below.

Discussions of GRB as cosmic ray sources are mainly oriented at exploring
their contribution to the energy range above EeV (1018 eV; e.g.
[492]),
referred to as ultra-high energy cosmic rays, or UHECRs.
(A model where GRB are responsible for CRs ranging from PeV to GZK is
[512]).
At EeV and higher energies the observed UHECR isotropy and the
small expected magnetic deflection suggests an extra-galactic origin. The
requirement that they are not attenuated by the cosmic microwave
background through photomeson interactions constrains that they are
originated within a volume inside a radius of 50-100 Mpc, the so-called
"GZK" volume (e.g.
[75]).
Two broad classes of models suggested are the "top-down" scenarios, which
attribute UHECR to decay of fossil Grand Unification defects, and the
"bottom-up" scenarios, which assume UHECRs are accelerated in astrophysical
sources. One of the most prominent candidate sources for bottom-up
scenarios is GRBs
[494,
482,
314]
(two others are AGNs, e.g.
[34]
and cluster shocks, e.g.
[208]).
The most commonly discussed version of this scenario considers the UHECR
to be protons accelerated in GRB internal shocks
[494,
493,
492],
while another version attributes them to acceleration in external shocks
[482,
481,
99].
(For UHECR acceleration in alternative GRB models, see, e.g.
[88,
117]).

The persuasiveness of this scenario is largely based on two coincidences,
namely, the required condition to accelerate protons
to GZK energies is similar to the requirement for generating the prompt
observed gamma-rays in GRB, and the observed UHECR energy injection rate
into the universe (~ 3 × 1044 erg Mpc-3
yr-1) is similar to the local GRB
-ray energy
injection rate
[494,
482].
These coincidences have been questioned, e.g.
[459,
445],
but these objections have been resolved using new data and further
considerations
[492,
481],
and GRBs remain a promising candidate
for UHECRs. However, there are some caveats of principle. The
internal shock scenario relies on the assumption that GRB prompt
gamma-ray emission is due to internal shocks. Although this is the leading
scenario, there is no strong proof so far, as is the case for the external
shock (e.g., there are efficiency and spectrum issues, etc.). On the
other hand, a Poynting flux dominated GRB model would have to rely on
magnetic dissipation and reconnection, accelerating electrons and hence
also accelerating protons- but details remain to be investigated. The
external shock model would have to rely on a magnetized medium
[481]
to reach the desired cosmic ray energy (as expected in pulsar wind bubbles
[236]
in the supranova scenario
[485],
which however has become
less likely since the almost simultaneous GRB 030329 / SN 2003dh and the more recent GRB 060218 / SN2006aj association).

Direct confirmation of a GRB orgin of UHECRs will be difficult. The next
generation cosmic ray detectors such as the Pierre Auger
Observatory
[14]
will have a substantially enhanced effective target area,
which will greatly improve the cosmic ray count statistics. This will help
to disentangle the two scenarios (top-down or bottom-up) and will reveal
whether a GZK feature indeed exists. Within the bottom-up scenario, the
directional information may either prove or significantly constrain the
alternative AGN scenario, and may eventually shed light on whether GRBs are
indeed the sources of UHECRs.

Internal shocks in the GRB jet take place at a radius
ri ~ 2
i2ct ~ 5
× 1012t-33002 cm. Here
i = 300
300 is
the bulk Lorentz factor of the GRB fireball ejecta and
t = 10-3t-3 s
is the variability time scale. Observed
-rays are
emitted from the GRB fireball when it becomes
optically thin at a radius
ri. Shock accelerated protons
interact dominantly with observed synchrotron photons with ~ MeV
peak energy in the fireball to produce a Delta resonance,
p+
[501].
The threshold condition to produce a
+ is
EpE = 0.2
i2 GeV2 in the observer
frame, which corresponds to a
proton energy of Ep = 1.8 × 107E, MeV-13002 GeV. The subsequent decays
+n+nµ+µne+eµµ produce high
energy neutrinos in the GRB fireball contemporaneous with
-rays
[501,
388].
Assuming that the secondary pions
receive 20% of the proton energy per interaction and each secondary lepton
shares 1/4 of the pion energy, each flavor of neutrino is emitted with
5% of the proton energy, dominantly in the PeV range.

The diffuse muon neutrino flux from GRB internal shocks due to proton
acceleration and subsequent photopion losses is shown as the short dashed
line in Fig. 10. The flux is compared to the
Waxman-Bahcall limit of cosmic neutrinos, which is derived from the
observed cosmic ray flux
[502].
The fluxes of all neutrino flavors are expected to
be equal after oscillation in vacuum over astrophysical distances.

The GRB afterglow arises as the jet fireball ejecta runs into the
ambient inter-stellar medium (ISM), driving a blast wave ahead into it
and a reverse shock back into the GRB jet ejecta. This (external)
reverse shock takes place well beyond the internal shocks, at a radius
re ~ 4e2ct ~ 2 ×
10172502t30 cm
[502].
Here e 250
250 is
the bulk Lorentz factor of the ejecta after the
partial energy loss incurred in the internal shocks and
t = 30
t30
s is the duration of the GRB jet. Neutrinos are
produced in the external reverse shock due to
p
interactions
of internal shock accelerated protons predominantly with synchrotron
soft x-ray photons produced by the reverse shock. The efficiency of
pion conversion from
p
interactions in this afterglow scenario
is much smaller than in the internal shocks
[502].

In the case of a massive star progenitor the jet may be expanding into
a wind, emitted by the progenitor prior to its collapse. In this case,
the density of the surrounding medium, at the external shock radius,
may be much higher than that typical ISM density of n 1 cm-3. For
a wind with mass loss rate of 10-5M
yr-1 and velocity of vw = 103
km/s, the wind density at the typical external shock radius would be
104
cm-3. The higher density implies a lower Lorenz factor of the
expanding plasma during the reverse shocks stage, and hence a larger
fraction of proton energy lost to pion production. Protons of energy
Ep 1018
eV lose all their energy to pion production in this scenario
[502,
484,
80]
producing EeV neutrinos.

As discussed before, the core collapse of massive stars are the most likely
candidates for long duration GRBs, which should lead to the formation of
a relativistic jet initially buried inside the star. The jet burrows through
the stellar material, and may or may not break through the stellar
envelope
[313].
Internal shocks in the jet, while it
is burrowing through the stellar interior, may produce high energy
neutrinos through proton-proton (pp) and photomeson
(p)
interactions
[396].
High energy neutrinos are
produced through pion decays which are created both in pp and
p
interactions. The jets which successfully penetrate through
the stellar envelope result in GRBs
(-ray
bright bursts) and the jets which choke inside the stars do not produce GRBs
(-ray dark
bursts). However, in both cases high energy
neutrinos produced in the internal shocks are emitted through the
stellar envelope since they interact very weakly with matter.

High energy neutrinos from the relativistic buried jets are emitted as
precursors (~ 10-100 s prior) to the neutrinos emitted from the
GRB fireball in case of an electromagnetically observed burst.
In the the case of a choked burst (electromagnetically undetectable) no
direct detection of neutrinos from individual sources is possible.
However the diffuse neutrino signal is boosted up in both scenarios.
The diffuse neutrino flux from two progenitor star models are shown in
Fig. 10, one for a blue super-giant (labeled H)
of radius
R* = 3 × 1012 cm and the
other a Wof-Rayet type (labeled He)
of radius R* = 1011 cm. The
Waxman-Bahcall diffuse cosmic ray bound
[503],
the atmospheric flux and the IceCube sensitivity to
diffuse flux are also plotted for comparison. The neutrino component
which is contemporaneous with the gamma-ray emission (i.e. which arrives
after the precursor) is shown as the dark dashed curve, and is plotted
assuming that protons lose all their energy to pions in
p
interactions in internal shocks.

Most GRBs are located at cosmological distances (with redshift z ~
1) and individual detection of them by km scale neutrino telescopes
may not be possible. The diffuse
flux is then dominated by a
few nearby bursts. The likeliest prospect for UHE
detection is
from these nearby GRBs in correlation with electromagnetic
detection. Detection of ultrahigh energy neutrinos which point back to
their sources may establish GRBs as the sources of GZK cosmic rays.

The detection of ultrahigh energy neutrinos by future experiments such as
ICECUBE
[207],
ANITA
[11],
KM3NeT
[225],
and Auger
[14]
can provide useful information, such as particle
acceleration, radiation mechanism and magnetic field, about the sources and
their progenitors. High energy neutrino astrophysics is an imminent
prospect, with Amanda already providing useful limits on the diffuse
flux from GRB
[457,
27]
and with ICECUBE
[3,
204,
189]
on its way. The detection of TeV and
higher energy neutrinos from GRB would be of great importance for
understanding these sources, as well as the acceleration mechanisms
involved. It could provide evidence for the hadronic vs. the MHD
composition of the jets, and if observed, could serve as an unabsorbed
probe of the highest redshift generation of star formation in the Universe.

The gamma-rays and the afterglows of GRB are thought to be produced
at distances from the central engine where the plasma has become optically
thin, r
1013 cm, which is much larger than the Schwarzschild
radius of a stellar mass black hole (or of a neutron star). Hence we have
only very indirect information about the inner parts of the central engine
where the energy is generated. However, in any stellar progenitor model
of GRB
one expects that gravitational waves should be emitted from the immediate
neighborhood of the central engine, and their observation should give
valuable information about its identity. Therefore, it is of interest to
study the gravitational wave emission from GRB associated with specific
progenitors. Another reason for doing this is that the present and
foreseeable sensitivity of gravitational wave detectors is such that
for likely sources, including GRB, the detections would be
difficult, and for this reason, much effort has been devoted to the
development of data analysis techniques that can reach deep into the
detector noise. A coincidence between a gravitational wave signal and a
gamma-ray signal would greatly enhance the statistical significance of the
detection of the gravitational wave signal
[125,
239].
It is therefore of interest to examine the gravitational wave signals
expected from various specific GRB progenitors that have been recently
discussed, and based on current astrophysical models, to consider the
range of rates and strains expected in each case, for comparison with
the LIGO sensitivity. A general reference is
[479],
which also discusses GRB-related sources of gravitational waves.

Regardless of whether they are associated with GRBs, binary compact
object mergers (NS-NS, NS-BH, BH-BH, BH-WD, BH-Helium star etc.)
[466,
372,
76,
239,
419,
215,
148,
229]
and stellar core-collapses
[389,
144,
90,
229,
475,
476,
477]
have been studied as potential gravitational wave (GW) sources.
These events are also leading candidates for being GRB progenitors, and
a coincidence between a GW signal and a gamma-ray signal would greatly
enhance the statistical significance of the former
[125].
A binary coalescence process can be divided into three phases: in-spiral,
merger, and ring-down
[124,
229].
For collapsars, a rapidly rotating
core could lead to development of a bar and to fragmentation instabilities
which would produce similar GW signals as in the binary merger scenarios,
although a larger uncertainty is involved. The GW frequencies of
various phases cover the 10 - 103 Hz band which is relevant
for the Laser Interferometer Gravitational-wave Observatory (LIGO)
[271]
and other related detectors such as VIRGO
[487],
GEO600
[158]
and TAMA300
[462].
Because of the faint nature of the typical GW strain, only
nearby sources (e.g. within ~ 200 Mpc for NS-NS and NS-BH
mergers, and within ~ 30 Mpc for collapsars)
[229]
have strong enough signals to be detectable by LIGO-II. When event rates
are taken into account
[147,
28],
order of magnitude estimates
indicate that after one-year operation of the advanced LIGO, one
event for the in-spiral chirp signal of the NS-NS or NS-BH merger, and
probably one collapsar event (subject to uncertainties), would be
detected
[229].
Other binary merger scenarios such as BH-WD and
BH-Helium star mergers are unlikely to be detectable
[229],
and they are also unfavored as sources of GRBs according to other
arguments
[339].

A time-integrated GW luminosity of the order of a solar rest mass
( 1054
erg) is predicted from merging NS-NS and NS-BH models
[239,
420,
321],
while the luminosity from collapsar models is more model-dependent, but
expected to be lower
([143,
318];
c.f.
[475]).
Specific estimates have been made of the GW strains from some of the
most widely discussed current GRB progenitor stellar systems
[229].
The expected detection rates of gravitational wave events with LIGO from
compact binary mergers, in coincidence with GRBs, has been estimated by
[125,
126].
If some fraction of GRBs are produced by DNS or
NS-BH mergers, the gravitational wave chirp signal of the in-spiral
phase should be detectable by the advanced LIGO within one year, associated
with the GRB electromagnetic signal. One also expects signals from
the black hole ring-down phase, as well as the possible contribution of
a bar configuration from gravitational instability in the accretion disk
following tidal disruption or infall in GRB scenarios.

The most promising GW-GRB candidates in terms of detections per year are
the DNS and BH-NS mergers
[229]
(Fig. 11), based on
assumed mean distances from the formation rates estimated by
[147].
More recent rate estimates are in
[479],
and rates incorporating new information relating to Swift short GRB
detections are in
[29,
328].
Other binary progenitor scenarios, such as black hole - Helium star and
black hole - white dwarf merger GRB progenitors are unlikely to be
detectable, due to the low estimates obtained for the maximum
non-axisymmetrical perturbations.

For the massive rotating stellar collapse (collapsar) scenario of GRB,
the non-axisymmetrical perturbations are very uncertain, but may be strong
[90,
144,
476],
and the estimated formation rates are much higher than for other progenitors
[144,
30],
with typically lower mean distances to the Earth. For such long GRB the rate
estimates must incorporate the beaming correction
[479].
This type of scenario is of special interest, since it has the most
observational support from GRB afterglow observations. For collapsars, in
the absence of detailed numerical 3D
calculations specifically aimed at GRB progenitors, estimates were made
[229]
of the strongest signals that might be expected in the case of
bar instabilities occurring in the accretion disk around the resulting
black hole, and in the maximal version of the recently proposed
fragmentation scenario of the infalling cores.
Although the waveforms of the gravitational waves produced in the
break-up, merger and/or bar instability phase of collapsars are not
known, a cross-correlation technique can be used making use of two
co-aligned detectors. Under these assumptions, collapsar GRB models
would be expected to be marginally detectable as gravitational wave
sources by the advanced LIGO within one year of observations.
Figure 11 depicts the characteristic GW strains
for the double neutrons star merger and the collapsar model.

Other calculations of massive stellar collapse GRB
[476,
477]
take into account MHD effects in the disk and BH.
More general studies of massive stellar core collapse event gravitational
wave emission are presented in
[146],
considering both core collapse SN and the progenitors of long GRB.

In the case of binaries the matched filtering technique can be used, while
for sources such as collapsars, where the wave forms are uncertain, the
simultaneous detection by two elements of a gravitational wave
interferometer,
coupled with electromagnetic simultaneous detection, provides a possible
detection technique. Specific detection estimates have been made
[229,
479]
for both the compact binary scenarios and the collapsar scenarios.

Both the compact merger and the collapsar models have in common
a high angular rotation rate, and observations provide evidence
for jet collimation of the photon emission, with properties depending on
the polar angle, which may also be of relevance for X-ray flashes.
Calculations have been made
[230]
of the gravitational wave
emission and its polarization as a function of angle expected
from such sources. The GRB progenitors emit l = m = 2
gravitational
waves, which are circularly polarized on the polar axis, while the +
polarization dominates on the equatorial plane. Recent GRB studies suggest
that the wide variation in the apparent luminosity of GRBs are caused by
differences in the viewing angle, or possibly also in the jet opening angle.
Since GRB jets are launched along the polar axis of GRB progenitors,
correlations among the apparent luminosity of GRBs
(L()
-2 and the
amplitude as well as the degree of linear polarization P
degree of the gravitational waves are expected, P4L-2. At a viewing angle larger than the jet
opening angle
j the GRB
-ray
emission may not be detected. However, in such cases an "orphan" (see, e.g.
[203,
531,
395])
long-wavelength afterglow could be observed, which would be preceded by a
pulse of gravitational waves with a significant linearly polarized
component. As the jet slows down and reaches
~
j-1,
the jet begins to expand laterally, and its electromagnetic radiation
begins to be observable
over increasingly wider viewing angles. Since the opening angle increases as
~ -1t1/2, at a viewing angle
>
j,
the orphan afterglow begins to be observed (or peaks) at a time
tp2 after the
detection of the gravitational wave burst.
The polarization degree and the peak time should be correlated as
Ptp2.

Gravitational wave burst searches are underway with LIGO. The results
from the third science run
[1]
searched for sub-second bursts in the
frequency range 100-1100 Hz for which no waveform model is assumed, with a
sensitivity in terms of the root-sum-square (rss) strain amplitude of
hrss ~ 10-20 Hz-1/2. No
gravitational-wave signals were detected
in the eight days of analyzed data for this run. The search continues, as
LIGO continues to be upgraded towards it ultimate target sensitivity.